Analysis and vibration of rectangular nanoplates - An overview (original) (raw)
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Strojnícky časopis – Journal of MECHANICAL ENGINEERING, 2019
This paper shows an analysis of the free vibration of functionally graded simply supported nanoplate. The nonlocal four variables shear deformation plate theory is used to predict the free vibration frequencies of functionally graded nanoplate simply supported using non-local elasticity theory with the introduction of small-scale effects. The effect of the material properties, thickness-length ratio, aspect ratio, the exponent of the power law, the vibration mode is presented, the current solutions are compared to those obtained by other researchers. Equilibrium equations are obtained using the virtual displacements principle. P-FGM Power law is used to have a distribution of material properties that vary across the thickness. The results are in good agreement with those of the literature. 1 Introduction Functionally graded materials attract the attention of many researchers because of their powerful uses and their characteristics (mechanical, chemical, thermal, physical) such as high abrasion resistance (ceramic face), high impact resistance, reactor components, and insulating joints. Dimming improves the toughness of the ceramic face and prevents ceramic-metal detachment. Functionally graded materials (FGM) can be characterized by the gradual variation of material properties in the thickness. A new type of composite materials is developed recently (Abdelbaki et al [1]; Arnab Choudhury et al [2]; Abdelbaki et al [3]; Ebrahimi and Barati [4]; Ebrahimi and Heidari [5]; Elmerabet et al [6]; Elmossouess et al [7]; Houari et al [8]; Karami et al [9]; Mahjoobi and Bidgoli [10]; Mohamed et al [11]; Mokhtar et al [12]; Mokhtar et al [13]; Sadoun et al [14]; Salari et al [15]; Shafiei and Setoodeh [16]; Shokravi [17]; Tlidji et al [18]; Tounsi et al [19]; Tu et al [20]; Bocko, J et al [21]; Jozef, B et al [22]; Stephan, K et al [23]; Murín, J et al [24]; Sapountzakis, E et al [25]). Research work dealing with the behavior of nanoplates under different types of loading can be cited as Ansari and Norouzzadeh [26] studied the buckling responses of circular, elliptical and asymmetric nanometric plates in FGM. Banh-Thien et al [27] presented a new numerical approach for the buckling analysis of non-uniform thick nanoplates in an elastic medium using isogeometric analysis (IGA). Ghadiri et al [28] studied the vibrational frequency of orthotropic monolayer graphene sheets embedded in an elastic medium under the effect of the change of temperature, or the solution for the vibration of orthotropic rectangular nanoplates under thermal effect and the elastic medium is obtained with using GDQM. Liu et al [29] studied buckling and post-buckling behaviors of piezoelectric nanoplates subjected to combined thermo-electro-mechanical charges based on non-local theory, Mindlin's plate theory and von Karman's geometric nonlinearity. Arefi and Zenkour [30] presented the thermo-electro-magneto-elastic bending analysis of a three-layer sandwich nanoplate based on Unauthentifiziert | Heruntergeladen 11.12.19 17:52 UTC
Beilstein journal of nanotechnology, 2013
In this article, a new higher order shear deformation theory based on trigonometric shear deformation theory is developed. In order to consider the size effects, the nonlocal elasticity theory is used. An analytical method is adopted to solve the governing equations for static analysis of simply supported nanoplates. In the present theory, the transverse shear stresses satisfy the traction free boundary conditions of the rectangular plates and these stresses can be calculated from the constitutive equations. The effects of different parameters such as nonlocal parameter and aspect ratio are investigated on both nondimensional deflections and deflection ratios. It may be important to mention that the present formulations are general and can be used for isotropic, orthotropic and anisotropic nanoplates.
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2017
Magneto-hygro-thermal vibration analysis of double-layered nanoplates made of functionally graded materials is presented based on higher order refined plate theory. For the first time, a double-layered nanoplate is modeled via nonlocal strain gradient theory in which both stiffness-softening and stiffness-hardening effects are incorporated. Another novelty of this paper is that the effects of magnetic and hygro-thermal fields on inhomogeneous double-layered nanoplates are considered to study their behavior under different physical fields. The gradation of material properties is considered using power-law model. The governing equations and related classical and non-classical boundary conditions are derived based on Hamilton's principle. These equations are solved for hinged nanoplates via Galerkin's method. It is indicated that type of vibration, moisture rise, temperature rise, nonlocal parameter, strain gradient parameter, material gradation, elastic foundation and side-to-thickness have a remarkable influence on vibration behavior of double-layered nanoscale plates.
2020
In this paper, the wave propagation method is combined with nonlocal elasticity theory to analyze the buckling and free vibration of rectangular Reddy nanoplate. Wave propagation is one of the powerful methods for analyzing the vibration and buckling of structures. It is assumed that the plate has two opposite edges simply supported while the other two edges may be simply supported or clamped. It is the first time that the wave propagation method is used for thick nanoplates. In this study, firstly the matrices of propagation and reflection are derived. Then, these matrices are combined to provide an exact method for obtaining the natural frequencies and critical buckling loads which can be useful for future studies. It is observed that obtained results of the wave propagation method are in good agreement with the obtained values by literature. At the end the obtained results are presented to evaluate the influence of different parameters such as nonlocal parameter, aspect ratio and...
Journal of Mathematical and Fundamental Sciences, 2022
In the present work, the equations of motion of a thin orthotropic nanoplate were obtained based on the new modified couple stress theory and the third-order shear deformation plate theory. The nanoplate was considered as a size-dependent orthotropic plate. The governing equations were derived using the dynamic version of Hamilton's principle and natural boundary conditions were formulated. An analytical solution in the form of a double Fourier series was obtained for a simply supported rectangular nanoplate. The eigenvalue problem was set and solved. It was analytically shown that the displacements of the median surface points in the plane of the plate do not depend on the material length scale parameters in the same directions; these in-plane directional displacements depend on the material length scale parameter in the out-of-plane direction only. On the other hand, the out-of-plane directional displacement depends on the length scale parameter in the plane directions only. The cross-section rotation angles depend on all length scale parameters. It was shown that the size-dependent parameters only have a noticeable effect on the deformed state of the plate if their order is not less than the order (plate height)-1 .
Vibration Analysis of a Rotating Nanoplate Using Nonlocal Elasticity Theory
Journal of Solid Mechanics, 2017
The nanostructures under rotation have high promising future to be used in nano-machines, nano-motors and nano-turbines. They are also one of the topics of interests and it is new in designing of rotating nano-systems. In this paper, the scale-dependent vibration analysis of a nanoplate with consideration of the axial force due to the rotation has been investigated. The governing equation and boundary conditions are derived using the Hamilton’s principle based on nonlocal elasticity theory. The boundary conditions of the nanoplate are considered as free-free in y direction and two clamped-free (cantilever plate) and clamped-simply (propped cantilever) in x direction. The equations have been solved using differential quadrature method to determine natural frequencies of the rotating nanoplate. For validation, in special cases, it has been shown that the obtained results coincide with literatures. The effects of the nonlocal parameter, aspect ratio, hub radius, angular velocity and di...
Buckling and vibration analysis nanoplates with imperfections
Applied Mathematics and Computation, 2019
In the present paper a coupling finite strip-finite element procedure is developed to investigate the buckling and vibration behaviour of imperfect nanoplates via nonlocal Mindlin plate theory. The imperfection can be either a thickness variation or a lack of planarity and it can be either localized or distributed on an entire edge of the nanoplate. The resulting nonlinear equations are solved exactly by applying the Kantorovich method. A finite element approach is proposed for coupling the in-plane and the out-of-plane buckling equations to describe properly the imperfections. Some numerical examples are carried out in order to show the sensitivity of the results to the nonlocal parameter and to the imperfection.
Size-dependent static characteristics of multicrystalline nanoplates by considering surface effects
International Journal of Mechanical Sciences, 2014
Nanostructures have been receiving extensive attention during the last two decades, due to their peculiar mechanical and other physical properties as compared with other macrostructures and macrosystems. The mechanical properties of nanostructures are intensely size-dependent. Furthermore, in the absence of external forces, nanostructures have a great tendency to deform due to their surface effects. Moreover, since the atoms on the surface have different equilibrium configuration from that of in the bulk, the elastic stiffness of the surface can be different from that of the bulk. In this study an ultra-thin plate of nanoscale thickness with an arbitrary geometry and boundary conditions is analyzed. A rectangular plate with nanoscale thickness is presented. In order to generalize the study, a multicrystalline plate with varying crystal properties has been assumed. Furthermore, the mechanical properties of the plate are dependent on the orientation. In fact the multicrystalline nanoplate is an anisotropic plate. The shapes and orientations of each crystal have been chosen haphazardly. However, the entire shape of the plate is a rectangle of microdimension with nanothickness. Due to the fact that silicon is much more applicable than any other material in Nanoelectromechanical systems (NEMS), it is assumed that the plate is made of silicon. The plate is subjected to a static load and the deformation as well as the corresponding strain is demonstrated. Due to the fact that the governing equation of the plate and its solution is not too straightforward to be solved easily, the finite element method is implemented so as to obtain the corresponding results. The results which have been achieved by the method of finite element and by employing the ANSYS software are illustrated and compared. Accordance of the results is quite remarkable.
International Journal of Mechanical Sciences, 2014
This paper, in line with the previous study , is concerned with the finite element implementation of nanoplates. However, in this contribution free vibration responses of multicrystalline nanoplates by considering surface effects are presented. Nanomaterials and nanostructures have been receiving widespread attentions during last decades. This fact is due largely to surprising, peculiar, and impressive mechanical; electrical; and physical behaviors of nanostructures. Currently, nanostructures such as nanoplates are being utilized in the designing and manufacturing Nanoelectromechanical systems (NEMS) and Microelectromechanical systems (MEMS). Furthermore, silicon, thanks to its exceptional mechanical, physical, and electrical properties is extensively employed in the NEMS and MEMS. The mechanical properties and responses of nanoplates are intensely size-dependent, and in contrast to plates with macro dimensions, static and free vibration responses of nanoplates strongly depend on the size of nanoplates. In this study, a rectangular multicrystalline plate with nanothickness; arbitrary geometry, and boundary conditions is analyzed. Each crystal of the nanoplate is assumed to be anisotropic, and a prominent point that must be taken into consideration is the interface region, which exists between every two crystals. The free vibration responses of nanoplate such as natural frequency are considered, and the influence of size, surface effects, interface region, and various boundary conditions over natural frequency of the nanoplate is considered. Due to the fact that geometry of the multicrystalline nanoplate is not straightforward to be dealt with the governing equations, the finite element method is employed to obtain the results of free vibration response. Moreover, we succeed to employ ANSYS software in order to attain the free vibration responses of multicrystalline nanoplates. In addition, the present finite element method results, the code of which is generated in MATLAB, are compared with those obtained from ANSYS software, and the correlation of the results is quite remarkable.
Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates
2020
In this paper, the free vibrations analysis of the nanoplates made of three-directional functionally graded material (TDFGM) with small scale effects is presented. To study the small-scale effects on natural frequency, modified strain gradient theory (MSGT) has been used. Material properties of the nanoplate follow an arbitrary function that changes in three directions along the length, width and thickness of the plate. The equilibrium equations and boundary conditions of nanoplate are obtained using the Hamilton's principle. The generalized differential quadrature method (GDQM) is used to solve the governing equations and different boundary conditions for obtaining the natural frequency of nanoplate made of three-directional functionally graded material. The present model can be transformed into a couple stress plate model or a classic plate model if two or all parameters of the length scales set to zero. Finally, numerical results are presented to study the small-scale effect ...